Question: Solve for $x$ and $y$ using elimination. ${x-5y = 5}$ ${-x+3y = -7}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x-5y = 5}\thinspace$ to find $x$ ${x - 5}{(1)}{= 5}$ $x-5 = 5$ $x-5{+5} = 5{+5}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {-x+3y = -7}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(1)}{= -7}$ ${x = 10}$